Matrix representation of a binary relation using fuzzy and artificial learning theory. An algorithm which uses the potential functions learning rule

Abstract

One of the most significant problems in economic domain is the dispose of human preference and choice forecasting. Recently, the economists have focused their researches to use the fuzzy concepts and the artificial learning procedures in the theory of economic choice. This paper extends the work done in this direction and offers a new algorithm for finding the matrix representation of the fuzzy binary relation which describes a preference relation.

Neuro-fuzzy concepts applied for planning of the cereal crops: applications to the maize hybrids growing in a Romanian region

“…The approach with fuzzy theory is justified by the fact that the preference relationship that has to be applied to the choice of the optimum variety can be rather considered an imprecise one because there are a number of criteria, factors such as climate and its consequences in the evolution of pests that require a vague character for the mathematical preference relation. Hence, we designed a sum fuzzy rational choice function C, which describes the choice behaviour from a set of alternatives X = {x 1 , x 2 , x 3 } when the preference relation r * is fuzzy binary [1].…”

“…Extending the work done in Badea et al [1] we design a new algorithm that gives M(r * ) with the following decision function:…”

“…To implement the algorithm we started from a Matlab computing achieved in Badea et al [1]. Here we used a different decision function, other than the potential function of the learning rule procedure.…”